Arithmetic on Polynomial Expressions Score: \( 0 / 10 \) Penalty: none Question If \( A=-2 x+8 \) and \( B=2 x-4 \), find an expression that equals \( 2 A+B \) in standard for Answer Attempt 1 out of 2

To find \( 2A + B \), we first evaluate \( 2A \) and \( B \): \[ 2A = 2(-2x + 8) = -4x + 16, \] \[ B = 2x - 4. \] Now we can combine these: \[ 2A + B = (-4x + 16) + (2x - 4) = -4x + 2x + 16 - 4 = -2x + 12. \] So, the expression \( 2A + B \) in standard form is \( -2x + 12 \). --- Did you know that polynomials have been studied for thousands of years? Ancient civilizations like the Babylonians and Greeks were already exploring polynomial equations as early as 2000 BC! They used these mathematical principles to solve practical problems, demonstrating that the love for mathematics transcends time and culture. In real life, polynomial expressions pop up more than you think! Engineers use polynomials to model physical systems — think of how they calculate the trajectory of a rocket or design roller coasters. Even when creating digital games, polynomials can help simulate how objects move and interact in a virtual environment, making your gaming experience thrilling!